An example of a direct multiplexed, root-mean-square (rms) responding electronic display is the well-known liquid crystal display (LCD). In such displays, a nematic liquid crystal material is positioned between two parallel glass plates having electrodes applied to each surface in contact with the liquid crystal material. The electrodes typically are arranged in vertical columns on one plate and horizontal rows on the other plate for driving a picture element (pixel) which are formed at the areas of overlap of each column electrode and each row electrode. A high information content display, e.g., a display used as a monitor in a portable laptop computer, requires a large number of pixels to portray arbitrary patterns of information. Matrix LCDs, for example, has 480 rows and 640 columns forming 307,200 pixels, and are widely used in computers today. Matrix LCDs with millions of pixels are expected soon.
In the so-called rms responding displays, the optical state of a pixel is substantially responsive to the square of the voltage applied to the pixel, i.e., the difference in the voltages applied to the electrodes on the opposite sides of the pixel. LCDs have an inherent time constant that characterizes the time required for the optical state of a pixel to return to an equilibrium state after the optical state has been modified by changing the voltage applied to the pixel. Recent technological advances have produced LCDs with time constants approaching the frame period used in many video displays (approximately 16.7 milliseconds). Such a short time constant allows the LCD to respond quickly and is especially advantageous for depicting motion without noticeable smearing of the displayed image.
Conventional direct multiplexed addressing methods for LCDs encounter a problem when the display time constant approaches the frame period. This problem occurs because conventional direct multiplexed addressing methods subject each pixel to a short duration "selection" pulse once per frame. The voltage level of the selection pulse is typically 7-13 times higher than the root-mean-square (rms) voltage averaged over the frame period. The optical state of a pixel in an LCD having a short time constant tends to return towards an equilibrium state between selection pulses resulting in lowered image contrast because the human eye integrates the resultant brightness transients at a perceived intermediate level. In addition, the high level of the selection pulse can cause alignment instabilities in some types of LCDs.
To overcome the above-described problems, an "active addressing" method has been developed. The active addressing method continuously drives the row electrodes with signals comprising a train of periodic pulses having a common period, T, corresponding to the frame period. The row signals are independent of the image to be displayed and preferably are orthogonal and normalized, i.e., orthonormal. The term orthogonal denotes that if the amplitude of a signal applied to one of the rows is multiplied by the amplitude of a signal applied to another one of the rows the integral of this product over the frame period is zero. The term normalized denotes that all the row signals have the same rms voltage integrated over the frame period.
During each frame period a plurality of signals for the column electrodes are calculated and generated from the collective state of the pixels in each of the columns. The column voltage at any time, t, during the frame period, T, is proportional to the sum obtained by considering each pixel in the column multiplying a "pixel value" representing the optical state (-1 representing fully "on", +1 representing fully "off", and values between -1 and +1 representing proportionally corresponding gray shades) of the pixel by the value of that pixel's row signal at time, t, and adding the products obtained thereby to the sum. If the orthonormal row signals switch between only two row voltage levels (+1 and -1), the above sum may be represented as the sum of the pixel values corresponding to rows having the first row voltage level, minus the sum of the pixel values corresponding to rows having the second row voltage level.
If driven in the active addressing manner described above, it can be shown mathematically that there is applied to each pixel of the display an rms voltage averaged over the frame period, and that the rms voltage is proportional to the pixel value for the frame. The advantage of active addressing is that it restores high contrast to the displayed image because instead of applying a single, high level selection pulse to each pixel during the frame period, active addressing applies a plurality of much lower level (2-5 times the rms voltage) selection pulses spread throughout the frame period. In addition, the much lower level of the selection pulses substantially reduces the probability of alignment instabilities.
A problem with active addressing results from the large number of calculations required per second. For example, a gray scale display having 480 rows and 640 columns, and a frame rate of 60 frames per second requires just under ten billion calculations per second. While it is of course possible with today's technology to perform calculations at that rate, the architecture proposed to date for calculation engines used for actively addressed displays have not been optimized to minimize power consumption. The power consumption and calculation speeds are issues of particularly importance to display units of portable devices which are powered by limited energy battery power supplies.
Thus, what is needed is a method and apparatus for performing calculations at high speeds while not increasing the power consumption for driving an actively addressed display.